denis tarasov et al- structural stability of clean, passivated, and partially dehydrogenated cuboid...

8/3/2019 Denis Tarasov et al- Structural Stability of Clean, Passivated, and Partially Dehydrogenated Cuboid and Octahedral

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Copyright 2011 American Scientific PublishersAll rights reservedPrinted in the United States of America

Journal ofComputational and Theoretical Nanoscience

Vol. 8, 121, 2011

Structural Stability of Clean, Passivated, and

Partially Dehydrogenated Cuboid and Octahedral

Nanodiamonds Up to 2 Nanometers in Size

Denis Tarasov1, Ekaterina Izotova2, Diana Alisheva2,

Natalia Akberova2, and Robert A. Freitas, Jr.3

1Kazan Branch of Joint Supercomputer Center, Russian Academy of Sciences, Kazan, 420111, Russia2Department of Biochemistry, Kazan State University, Kazan, Tatarstan, 420008, Russia

3Institute for Molecular Manufacturing, Palo Alto, CA 94301, USA

The use of precisely applied mechanical forces to induce site-specific chemical transformationsis called positional mechanosynthesis, and diamond is an important early target for achieving

mechanosynthesis experimentally. The next major experimental milestone may be the mechanosyn-

thetic fabrication of atomically precise 3D structures, creating readily accessible diamond-based

nanomechanical components engineered to form desired architectures possessing superlative

mechanical strength, stiffness, and strength-to-weight ratio. To help motivate this future experi-

mental work, the present paper addresses the basic stability of the simplest nanoscale diamond

structurescubes and octahedrapossessing clean, hydrogenated, or partially hydrogenated sur-

faces. Computational studies using Density Functional Theory (DFT) with the Car-Parrinello Molec-

ular Dynamics (CPMD) code, consuming 1,466,852.53 CPU-hours of runtime on the IBM Blue

Gene/P supercomputer (23 TFlops), confirmed that fully hydrogenated nanodiamonds up to 2

nm (9001800 atoms) in size having only C(111) faces (octahedrons) or only C(110) and C(100)

faces (cuboids) maintain stable sp3 hybridization. Fully dehydrogenated cuboid nanodiamonds

above 1 nm retain the diamond lattice pattern, but smaller dehydrogenated cuboids and dehydro-

genated octahedron nanodiamonds up to 2 nm reconstruct to bucky-diamond or onion-like car-bon (OLC). At least three adjacent passivating H atoms may be removed, even from the most

graphitization-prone C(111) face, without reconstruction of the underlying diamond lattice.

Keywords: Carbon, Cuboid, Bucky-Diamond, Diamond, Dehydrogenation, DFT, Dimerization,DMS, Fullerene, Hydrogen, Mechanosynthesis, Nanodiamond, Nanotechnology,

Octahedron, OLC, Reconstruction, Stability.

CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1. Clean Nanocarbon . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2. Fully Hydrogenated Nanocarbon . . . . . . . . . . . . . . . . . 41.3. Partially Dehydrogenated Nanocarbon . . . . . . . . . . . . . 5

2. Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . 83. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . . . . . 9

3.1. Clean and Hydrogenated Nanodiamond Octahedrons . . . . 93.2. Clean and Hydrogenated Nanodiamond Cuboids . . . . . . 133.3. Dimerization Patterns on Nanodiamond C(100) Faces . . . 143.4. Partial Dehydrogenation of Nanodiamond Surfaces . . . . . 15

4. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Author to whom correspondence should be addressed.

1. INTRODUCTION

Arranging atoms in most of the ways permitted by physical

law is a fundamental objective of molecular manufactur-ing. A more modest and specific objective is the abil-ity to synthesize atomically precise diamondoid structuresusing positionally-controlled molecular tools. Such posi-tional control might be achieved using an instrument likea Scanning Probe Microscope (SPM).

The use of precisely applied mechanical forcesto induce site-specific chemical transformations usingpositionally-controlled highly reactive tools is called posi-tional mechanosynthesis. In 2008, Freitas and Merkle1

reviewed all known theoretical studies of positional dia-mond mechanosynthesis (DMS). They proposed the first

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Structural Stability of Clean, Passivated, and Partially Dehydrogenated Cuboid and Octahedral Nanodiamonds Tarasov et al.

complete set of DMS reaction sequences and an associ-ated minimal set of nine specific SPM-based DMS tooltipsoperating in vacuum that could be used to build cubicand hexagonal diamond lattices of process-unlimited size,graphene sheets (e.g., carbon nanotubes) and polyynechains, and all of the tools themselves including all neces-sary tooltip recharging reactions, virtually atom by atom,

using only the elements C, Ge and H. In 2009 Tarasovet al.2 completed the first extensive DMS tooltip trajec-tory analysis, examining a wide range of viable multiple

Denis Tarasov is Senior Research Scientist at the Kazan Branch of Joint SupercomputerCenter, Russian Academy of Sciences, in Kazan, Russia. He graduated from the Depart-ment of Biochemistry of Kazan State University in Kazan (Russian Federation) and receivedan M.S. in biochemistry. He was awarded his Ph.D. in Biology from Kazan State Univer-sity in 2004. His research interests include computer modeling in biology and chemistry,high performance computing, and molecular machine systems. He has 15 refereed journalpublications.

Ekaterina Izotova is a Ph.D. candidate in Kazan State University with research interestsin molecular mechanics and quantum chemistry methods. She was born in Kazan (Russia)and received her M.S. in biochemistry from Kazan State University.

Diana Alisheva is a Ph.D. candidate at the Kazan State University with research interests inmolecular mechanics, quantum chemistry and computer graphics for scientific visualization.She was born in Kazan (Russia) and received her M.S. in biochemistry from Kazan StateUniversity.

Natalia Akberova is Assistant Professor of the Kazan State University biology depart-ment. She has a Ph.D. in Biology, with specialization in biochemistry (1999) and lecturerof courses for biology department students in informatics, bioinformatics, and modelingin biology. Her scientific interests include systems biology, bioinformatics, and molecularmodeling.

degrees-of-freedom tooltip motions in 3D space that couldbe employed to recharge the hydrogen abstraction tool, akey reaction set in DMS.

The landmark experimental demonstration of posi-tional atomic assembly occurred in 1989 when Eiglerand Schweizer3 employed an SPM to spell out the IBMlogo using 35 xenon atoms arranged on nickel surface,

though no covalent bonds were formed. In 2003, Oyabuet al.4 achieved the first experimental demonstration ofatomically precise purely mechanical positionalchemical

2 J. Comput. Theor. Nanosci. 8, 121, 2011


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Tarasov et al. Structural Stability of Clean, Passivated, and Partially Dehydrogenated Cuboid and Octahedral Nanodiamonds

Robert A. Freitas, Jr. is Senior Research Fellow at the Institute for Molecular Manufactur-ing (IMM) in Palo Alto, California, and was a Research Scientist at Zyvex Corp. (Richard-son, Texas), the first molecular nanotechnology company, during 20002004. He receivedB.S. degrees in Physics and Psychology from Harvey Mudd College in 1974 and a J.D. fromUniversity of Santa Clara in 1979. Freitas authored in 1996 the first detailed technical designstudy of a medical nanorobot ever published in a peer-reviewed mainstream biomedical jour-

nal, followed by Nanomedicine (Landes Bioscience, 1999, 2003; www.nanomedicine.com),the first book-length technical discussions of the potential medical applications of molec-ular nanotechnology. He has 49 refereed publications, serves on the Editorial Boards of 9medical or nanotech journals, co-authored the book Kinematic Self-Replicating Machines(Landes Bioscience, 2004; www.molecularassembler.com/KSRM.htm), co-founded in 2006

the Nanofactory Collaboration (www.molecularassembler.com/Nanofactory) to build the first working nanofactory foratomically precise manufacturing, won the 2009 Feynman Prize in nanotechnology for theory, and in 2010 was awardedthe first U.S. patent on diamond mechanosynthesis. His home page is at www.rfreitas.com.

synthesis on a heavy atom using only mechanical forcesto make and break covalent bonds, first abstracting andthen rebonding a single silicon atom to a silicon surface

with SPM positional control in vacuum at low temperature.Using an atomic force microscope the same group simi-larly manipulated individual Ge atoms in 2004 and Si/Snand Pb/In atoms in 2008.56

The next major experimental milestone may be themechanosynthetic fabrication of atomically precise 3Dstructures, creating readily accessible diamond-basednanomechanical components engineered to form desiredarchitectures possessing superlative mechanical strength,stiffness, and strength-to-weight ratio. These nanoscalecomponents may range from relatively simple diamondcubes, rods or rings to more sophisticated nanoparts

such as fullerene bearings,79 gears1012 and motors,13composite fullerene/diamond structures,14 and more com-plex devices15 such as diamondoid gears,16 pumps,16 andconveyors.17 To help motivate this future experimentalwork, the present paper addresses the basic stability ofthe simplest nanoscale diamond structurescubes andoctahedrapossessing clean, hydrogenated, or partiallyhydrogenated surfaces.

1.1. Clean Nanocarbon

Macroscale diamond has long been known to be ther-

modynamically stable with respect to graphite only athigh pressure. At room temperature and pressure, graphiteis stable but diamond is only metastable with respectto graphitethat is, the diamond is slowly graphitizing.Room-temperature diamond is only 0.02 eV (kBT)higher in energy than graphite but a large activation bar-rier inhibits the transformation,18 so macroscale diamond,once formed near or below room temperature, will notreadily transform into graphite. However, for a sufficientlysmall carbon cluster, nanodiamond can be more stable thannanographite because of the small molar volume of dia-mond compared to that of graphite.19 As particle size falls

deeper into the nanoscale, graphite and diamond phasescan sometimes co-exist with, or even be co-opted by,other forms of pure carbon, particularly (A) onion-like car-

bon or OLC (multi-shelled nested fullerenes)20 and (B)bucky-diamond (a diamond core up to a few nanome-ters wide surrounded by a partially or completely delam-inated fullerenic outer shell),21 an intermediary betweennanodiamond and OLC. There appear to be three distinctthermodynamic regimes for pure carbon nanoparticles asa function of size:1922

(1) The size range above 510 nm is most likely thegraphitic regime wherein the graphite phase is thermo-dynamically preferred and the nanodiamond phase ismetastable relative to graphite, but where nanodiamond,once formed (e.g., from sp3-bonded amorphous carbon

clusters),23 will not readily transform into graphite at mod-erate or low temperatures in any practical time period.(2) The size range from 1.52 nm up to 510 nm isthe nanodiamond regime in which the diamond phase isthermodynamically the most stable form for pure car-bon nanoparticles. Gamarnik2425 used a thermodynamicmodel to calculate the size-dependent threshold preferencefor stable pure carbon nanodiamond over nanographiteas 10.2 nm at 25 C, 6.1 nm at 545 C, 4.8 nm at800 C, and 4.3 nm at 1100 C. Jiang et al.26 mod-eled the phase transition thermodynamics between nanodi-amond and nanographite including the effects of surface

stress on the internal pressure of the nanoparticle, andfound the transition size to nanodiamond decreases from11 nm at 0 K to 4 nm at 1500 K; they note the exper-imental observation that 5 nm nanodiamonds are trans-formed into nanographite at 1073 K. (Carbon implantationexperiments27 also suggest that diamond is the stable formof carbon for crystallites


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computational method used), corresponding to a particlesize of 68 nm; in another study using other methods,Barnard et al.22 estimated 24,398 atoms (5.2 nm) as theupper limit. Note that this size range for nanodiamond sta-bility does not represent the only size regime in whichnanocrystalline diamond may be formed; it simply indi-cates that outside of this range the nanodiamonds will be

metastable with respect to a transformation to graphitic orfullerenic phases.19

(3) The nanoparticle size range of 1.52 nm and smalleris the fullerenic regime, in which pure carbon nanopar-ticles will spontaneously form OLC or else the diamondand fullerene phases will co-exist as bucky-diamonds. ADFT (Density Functional Theory)-based study by Wenet al.30 found that the crossover from sp3 (nanodiamond)to sp2 (fullerenic) stability occurs at ncarbon 1060 atoms(2.1 nm). Barnard et al.22 also investigated the phasestability of these smaller nanocarbon particles by mod-eling the enthalpy of formation for relaxed, dehydro-

genated (stable) nanodiamond crystals and fullerenes. Theresults indicated crossover to a more stable fullerenicphase below 1100 atoms, equivalent to cubic nanodi-amond crystals 1.9 nm in diameter and correspondingroughly to the experimentally observed minimum nanodi-amond particle size;31 this cutoff size was later confirmedby Barnard and Sternberg32 using DFTB (density func-tional based tight binding). A review33 of the literatureregarding the structure of carbon nanoparticles indicatesthat other carbon forms such as fullerenes and onion-like carbon (OLC) are abundant at sizes below 1.8 nm.For example, one comparison34 of the relative stability of

60540 atom fullerenes and closed carbon nanotubes usingfirst-principles pseudopotential calculations, predicted (inagreement with experimental observations) that a 1.3 nmdiameter nanotube is energetically preferred among thevarious SWNTs and fullerenes examined. Note that phasetransitions in a coexistence regime35 are not entirely ther-modynamically driven; other factors such as surface ener-gies, surface stress and charge, and kinetic considerationsincluding direct mechanochemical forces may be instru-mental in inducing a change of phase.19

There are three sub-regimes within the fullerenicregime.35 In the range of 500900 atoms (1.41.7 nm),

OLC is the most stable form of pure nanocarbon; from9001350 atoms (1.72.0 nm), bucky-diamond and OLCcoexist; and between 13501850 atoms (2.02.2 nm),bucky-diamond and nanodiamond coexist. The intersec-tion of the bucky-diamond and OLC stability was foundto be very close to the intersection for nanodiamondsand fullerenes at 1100 atoms (1.9 nm), suggestingthat above this size an sp3-bonded core becomes morefavorable than a sp2-bonded core, irrespective of surfacestructure.35 It was also determined using semiempirical36

and first principles methods37 that the nanodiamond-to-onion phase transition is initiated by the presence of the

diamond C(111) surface, and does not occur on the C(110)and C(100) surfaces.38

A related study by Barnard and Snook39 found thatsingle-walled carbon nanotubes are the most energeticallypreferred form for 1-D pure nanocarbon structures, but thatthere may exist a narrow window of stability for nonhy-drogenated diamond nanowires between about 450 atoms

(2.7 nm diameter) and 870930 atoms (3.73.9 nm) perunit length. Ab initio analysis shows that the C(110) andC(100) surfaces of diamond nanowires remain stable in thesp3 configuration40 (though exhibiting significant changesin the length and cross-sectional area) but the C(111) sur-faces delaminate to form nano-tubular cages, running par-allel to the nanowire axis, called bucky-wires (analogousto bucky-diamonds),41 with chiral structures identical tothat of an armchair carbon nanotube.42

1.2. Fully Hydrogenated Nanocarbon

In the case of fully-hydrogenated carbon nanoparticles, theaddition of passivating hydrogen atoms is not expected toreduce the preferential stability of nanodiamonds in the1.52.0 nm up to 510 nm size range or the metastabilityof nanodiamonds relative to nanographite in the 510 nmand larger size range. The remaining uncertainty pertainsto the smallest size range, 2 nm and below.

In 2003 Raty and Galli43 used first-principles calcu-lations (based on formation energy, with terms for thevibrational and the total energy of a nanoparticle obtainedusing DFT) to examine the relative stability of


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ambient (or low) pressure and temperature conditions. Forexample:(1) In 1998 Winter and Ree28 used the AM1 and PM3parameterizations of the semi-empirical modified neglectof diatomic overlap (MNDO) method to optimize thegeometry of diamond clusters (C10, C35, C84, C165, and C286octahedral nanodiamonds), both for pure carbon forms andfor structures whose dangling bonds were capped withhydrogen. In all cases, the surface instability observedafter relaxing the dehydrogenated clusters was eliminated,the diamond structure was preserved throughout, and theoptimized (relaxed) H-passivated diamond clusters gavesp3 CC bond lengths very close to the experimental valueof 1.54 .(2) Similar results were obtained by Barnard et al.3744

in 2003 as part of a more rigorous first-principlesstudy of cubic (C28H32, C54H48, a nd C259H140, octa-hedral (C35H36, C84H64, and C165H100, and cuboctahe-dral (C29H24, C142H72, and C323H124 nanodiamonds up to1 nm in diameter. Calculations were performed withVASP using DFT within the generalized gradient approx-imation (GGA) and the Perdew-Wang (PW91) exchange-correlation functional with ultrasoft, gradient-corrected,Vanderbilt-type pseudopotentials. Comparison of the car-bon framework of the relaxed dehydrogenated and hydro-genated versions of the same nanodiamonds confirmsthat hydrogenated octahedrons are stable at 0 K withhydrogenation eliminating the transformation to bucky-diamond, and that H-passivated nanodiamonds are char-acterized by more bulk-diamond-like properties such ascohesive energy44 and surface structure.38 (All octahedron

faces are C(111) crystal planes, the surface most prone tographitization.) The retention of sp3 bonding in the pas-sivated nanodiamonds was confirmed via calculation ofWannier functions (local bond-centered functions ratherthan atom-centered ones)dehydrogenated structures con-tained distorted - and -bonds while their hydrogenatedcounterparts were found to be entirely -bonded4445andvia DFT (VASP) in a related study.42

(3) In 2004, Barnard46 showed that hydrogenation elimi-nates C(111) surface delamination of diamond nanowires.Hydrogenation of the cuboctahedral C168H72 and octa-hedral C186H96 diamond nanowire surfaces reduced the

expansions and contractions of the nanowire segmentlength and cross-sectional area exhibited by their dehy-drogenated (C168 and C186 counterparts.

41 Hydrogena-tion even stabilized otherwise unstable B- and N-dopedcuboctahedral (C29H24 and Al-, O-, and P-doped cubo-dodecahedral (cylindrical) (C63H36 diamond nanowiresegments.4748

(4) In 2005, Laikov and Ustynyuk49 benchmarkedPRIRODA-DFT using the fully-hydrogenated nanodia-mond tetrahedrons C26H32, C51H52, C87H76, C136H104,C200H136, C281H172 and C381H212 (2 nm edge), and foundno indication of lattice reconstruction.

(5) In 2006, Lewandowski and Merchant50 found thathydrogenating 1.21.8 nm diamond nanowires, simu-lated at 300 K using Car-Parrinello Molecular Dynamics,removes all mechanical flexibility and stabilizes the dia-mond structure.(6) In 2007, Wen et al.30 applied all-electron DFT cal-culations to a series of hydrogenated octahedrons up to

C455H196, finding these structures to be stable and pos-sessing a negative heat of formation (i.e., exothermic) forncarbon < 752 atoms (1.9 nm). As the hydrogenated nan-odiamond size increased, the average CC bond lengthrose slightly from 1.5407 for C35H36 (0.7 nm) to1.5432 for C455H196 (1.7 nm), slowly approaching theCC bond length of 1.5471 for bulk diamond crystal atthe PW91/DNP level of theory.30

Experimentally, there are many examples of very sta-ble and very small sp3-bonded hydrogen-terminated car-bon nanoparticles in the 1 nm range, in particular thehydrocarbon cage molecules known as diamondoids thatoccur in natural petroleum, from single-cage adamantane(C10H16 to the multi-cage polymantanes (e.g., 11-cageundecamantane, 100 atoms, 1 nm).51 An experimentalstudy found that hydrogen termination of 220 nm nan-odiamond crystallites prevents their graphitization underextreme UV irradiation.52 Plasma hydrogenation of multi-walled carbon nanotubes converts them to bucky-diamond,the core becoming cubic or hexagonal nanodiamonddepending on the relative chiralities of the innermost nano-tube shells.53 Barnard19 suggests that even if H-terminatednanodiamonds were slightly higher in energy than theirdehydrogenated counterparts, the nanodiamonds might still

be metastable below the hydrogen desorption temperature,thus preventing spontaneous (size-dependent) hydrogendesorption and recombination in the absence of a suitablekinetic factor such as the activation energy required forhydrogen desorption.

Pragmatic experimentalists sometimes complain thatnanodiamonds oxidize and that fully (or partially) hydro-genated surfaces are unrealistic, but nanodiamonds inthe DMS context are intended to be fabricated in alargely oxygen-free UHV environment using a controlledsequence of 1-, 2- or 3-atom site-specific mechanosyn-thetic transfers from an atomically precise tooltip. In com-

putational nanoscience, H is a generic passivant atom andthe stability of the underlying lattice structure of a nanodi-amond depends almost entirely on the general presence orabsence of passivation, and far less on the nature of thespecific passivating species used.

1.3. Partially Dehydrogenated Nanocarbon

The effect of partial dehydrogenation on nanoparticle sta-bility has yet to be seriously addressed. During DMS, oneor two neighboring radical sites must be created on a grow-ing passivated nanodiamond workpiece (e.g., by removing

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one or two H atoms using a positionally-controlled hydro-gen abstraction tool) in preparation for the next step ina DMS reaction sequence for building diamond latticesuch as the site-specific addition of a methyl group tothe new radical site, or the use of radicalradical cou-pling to bond two radical sites, using another positionally-controlled DMS tool.

Cubic diamond has three principal or high-symmetrycleavage planesthe C(110), C(100) and C(111) crystal-lographic faces.

The clean C(110)(11) diamond surface (Fig. 1(A)),which consists of zigzag chains of carbon atoms havingsome -bond character (bondlength 1.43 ),54 does notreconstruct after annealing even to >1300 K55 though suchhigh temperatures may begin to induce graphitization.56

Heating the hydrogen-terminated C(110)H(1 1) sur-face (Fig. 1(B)) to >1400 K yields a dehydrogenatedclean but unreconstructed C(110)(11) surface,57 withthe CC bondlength in the zigzag chain increasing to

1.51 .54 Hence partial dehydrogenation of passivatedC(110) should not cause lattice reconstruction.

The clean C(100)(11) diamond surface (Fig. 1(C))has two dangling bonds per exposed carbon atom,an unstable surface that immediately reconstructs to aC(100)(21) pentagonal-ring geometry via the formationof rows of symmetric -bonded (double-bonded) dimers.58

(A) (B)

(C) (D)

(E) (F)

Fig. 1. Principal diamond surfaces: (A) C(110)(1 1); (B) C(110)H(1 1); (C) unstable C(100)(1 1); (D) reconstructed C(100)H(2 1);(E) C(111)H(11) glide plane; (F) C(111)(21) Pandey reconstruction. (C = black, H=white).

(Graphitization of C(100) occurs readily >1600 K59 but ismore difficult than for C(110).60 Addition of 1 H atomper dimer carbon atom, a 1.0 ML (monolayer) surface cov-erage, increases dimer bondlength from 1.37 (C C) to1.61 (CC) but leaves the existing lattice reconstruc-tion intact (Fig. 1(D)).58 (In theory a dihydride (2.0 ML)

could de-reconstruct the C(100) surface but its existenceis controversial, and the monohydride may be energeti-cally preferred and more stable against spontaneous CH4formation;61 1.25 ML,62 1.33 ML,63 1.5 ML,58 1.75 ML,62

and other polyhydrides6264 have also been proposed.) Par-tial dehydrogenation of monohydride-passivated C(100)H(2 1) surface should not alter the existing latticereconstruction geometry.

A clean C(111) diamond surface that is passivated witha saturated monolayer (1.0 ML) of H atoms exhibitsa stable C(111)H(1 1) monohydride hexagonal lat-tice structure (Fig. 1(E)) that does not reconstruct atroom temperature.65 Upon heating in vacuo sufficientlyto remove the passivating hydrogen (8001100 K),66

the carbon atoms at the C(111)(1 1) shuffle plane(one dangling bond per exposed tri-bonded carbon atom)surface undergo reconstruction into a new stable sp2

bonding structure with C(111)(2 1) symmetry called



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the Pandey reconstruction,67 a rearrangement energeticallyfavored by 0.30.7 eV6869 with a low or zero transi-tion barrier.70 In the Pandey reconstruction (Fig. 1(F)), thepuckered-hexagon layer of the ideal (111) surface is trans-formed into planar zigzag chains of carbon atoms, alter-nately raised and lowered, in a conformation not unlike theideal (110) surface. The connectivity to the next layer of

underlying atoms is affected, with the formation of alter-nating five- and seven-membered rings71 and -bondedchains arising in the first upper two layers67 (which useup the unsatisfied valencies or dangling bonds). Furtherheating of the Pandey surface causes graphitization,69 theseparation of the uppermost layer from the lower lay-ers analogous to bucky-diamond, whereas rehydrogenationrecovers the original C(111)H(11) surface (i.e., Pandeyreconstruction is reversible).

Uncertainty exists in the experimental literatureabout the exact threshold fraction of hydrogen surfacecoveragee.g., 0.50 ML,7274 0.33 ML,78 0.20 ML,79 or

(A) (B)

Fig. 2. Schematic representations of initial un-relaxed structures cleaved from a diamond lattice, showing examples of (A) octahedral (all C(111)faces) and (B) cuboid (C(110) and C(100) faces) shapes. For clarity, only un-reconstructed surface atoms are shown in the wire-frame images (bottom),where the color (red = C(111), blue= C(110), green = C(100)) corresponds to the crystallographic orientation as indicated by the geometric images(top); redrawn from Barnard and Sternberg;32 images courtesy Damian G. Allis, Syracuse University.

less7477required to suppress all Pandey reconstructionof the C(111) surface and maintain the sp3 (11) struc-ture across the entire surface. A first-principles dynam-ical simulation by Jackson80 of two adjacent danglingcarbon bonds on an otherwise hydrogen-saturated diamondC(111) surface, using a simple cluster model, providedearly theoretical evidence that two adjacent dangling sur-

face bonds might be stable (i.e., a localized 0.33 MLthreshold). The study found that the two dangling-bondcarbon atoms relaxed slightly into the surface, enhancingtheir bonding with the subsurface carbon atoms and short-ening their bond lengths to these atoms from 1.54 to1.41 , while at the same time the two dangling-bond car-bon atoms showed no tendency to enhance their bondingto each other which could lead to surface reconstruction.A subsequent study by Barnard et al.42 performed withVASP using DFT and GGA/PW91 with ultrasoft, gradient-corrected, Vanderbilt-type pseudopotentials examined there-lamination of an exfoliated C(111) surface consisting



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of a diamond slab 12 atomic layers thick and an exfoli-ated sheet 2 atomic layers thick onto which single atomichydrogens were successively but randomly chemisorbed.Re-lamination of the sheet reaches 100% sp3 bonding at0.500.60 ML, suggesting that removing one passivating Hatom from a C(111)H(11) surface during DMS shouldnot disrupt the diamond lattice; the re-laminating sheetreaches 60% sp3 at 0.33 ML, so a lattice-nondisruptiveremoval of two adjacent H atoms on C(111)H(11) alsoseems possible.

2. COMPUTATIONAL METHODS

Graphitization of nanodiamond to form bucky-diamond,bucky-wire or OLC is least likely on C(110) and C(100)faces and most likely on C(111) faces, so our study ofstructural stability focuses on nanoparts of two kinds. Atthe one extreme is structures having cuboid (or, equiva-

lently, rectangular prism) geometry (Fig. 2(A)). These canbe designed using only C(110) and C(100) faces and noC(111) faces, hence should present the easiest case fornanodiamond stability. At the other extreme is structureshaving octahedral geometry consisting entirely of C(111)

Table I. Cuboid and octahedron nanodiamonds.

Cuboids Octahedra

Dimensions () Dimensions ()File Total # Chemical File Total # Chemicalname atoms formula X Y Z name atoms formula Edge Diagonal

Dehydrogenated (clean) diamond Dehydrogenated (clean) diamondCube33 21 C21 3.7 3.9 5.5 Octa22 10 C10 2.5 3.6Cube44 46 C46 4.8 5.1 5.5 Octa44 35 C35 5.1 7.1Cube55 65 C65 6.2 6.3 7.0 Octa66 84 C84 7.5 10.6Cube66 104 C104 7.5 7.5 7.0 Octa88 165 C165 10.1 14.2Cube77 168 C168 8.8 8.9 8.7 Octa1010 286 C286 12.6 17.8Cube88 246 C246 9.9 10.0 10.5 Octa1212 455 C455 15.1 21.4Cube99 297 C297 11.1 11.3 10.5 Octa1414 680 C680 17.7 25.0Cube1010 428 C428 12.6 12.6 12.8Cube1111 600 C600 13.9 13.9 14.1Cube1212 693 C693 15.1 15.1 14.1Cube1313 891 C891 16.4 16.5 16.0Cube1414 1167 C1167 17.6 17.7 17.8Cube1515 1328 C1328 19.0 19.0 17.8

Fully passivated (hydrogenated) diamond Fully passivated (hydrogenated) diamondCube33H 47 C21H26 5.6 5.7 7.3 Octa22H 26 C10H16 4.3 5.0Cube44H 94 C46H48 6.8 6.8 7.4 Octa44H 71 C35H36 6.8 8.5Cube55H 117 C65H52 8.1 8.3 9.0 Octa66H 148 C84H64 9.4 12.1Cube66H 180 C104H76 9.4 9.4 9.0 Octa88H 265 C165H100 12.0 15.7Cube77H 272 C168H104 10.6 10.7 10.9 Octa1010H 400 C286H114 14.5 19.3Cube88H 380 C246H134 11.9 11.9 12.5 Octa1212H 651 C455H196 17.0 22.9Cube99H 445 C297H148 13.3 13.3 12.5 Octa1414H 936 C680H256 19.6 26.5Cube1010H 628 C428H200 14.8 14.8 14.3Cube1111H 852 C600H252 15.9 15.9 16.2Cube1212H 965 C693H272 17.1 17.2 16.2Cube1313H 1211 C891H320 18.4 18.5 18.1Cube1414H 1571 C1167H404 19.7 19.7 20.4Cube1515H 1760 C1328H432 21.0 21.0 20.4

faces and no C(110) or C(100) faces (Fig. 2(B)), repre-senting the greatest challenge for nanodiamond stability.

The initial structures for a representative series of octa-hedral and cuboid nanodiamond nanoparts up to 2 nm insize (Table I) were carved from a larger diamond slab thatwas energy-minimized using MM+ in HyperChem. Theoctahedrons are well-defined in size and shape because

C(111) is the natural cleavage plane and all faces areof the same type. The cuboids are not exactly perfectcubes because two different crystal faces intersect, hencethere is choice in the precise number of atomic layersand in the termination geometries to be employed for theC(100) faces at the top and bottom of each cuboid. Keep-ing all 3 dimensions as equal as possible, a series of13 cuboids were produced by rotating the diamond lat-tice until a tessellation pattern appeared from above theC(100) plane, then counting the number of squares alongeach edge defining the nanodiamond in this plane (e.g.,Cube15 15 results from carving out a chunk of lattice

measuring 15 squares on an edge). Each square is roughlyhalf the width of an adamantane cage. For all 13 cuboidsand 7 octahedrons, both hydrogenated and unhydrogenatedcases, we computed the minimum energy geometry andexamined the results for changes in bond length, structural



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rearrangements, graphitization, or other evidence of struc-tural instability.

For C(100) surfaces on cuboids with an even numberof north-south dimerizable rows (Fig. 1(C)), fabricationvia positionally-controlled DMS allows the surface to bemanufactured with a uniform pattern of dimers such thatall dangling bonds are consumed (Fig. 1(D))presumablythe global minimum on the PES. This is not possiblefor C(100) cuboid faces having an odd number of north-south dimerizable rows (Cube66H, Cube1010H, andCube1414H) because in such cases one north-south rowwill be unpaired, giving rise to a variety of possible dimer-ization patterns. To determine the energetically preferreddimerization pattern, we performed structure optimizationson all dimerization patterns for Cube66H (3 north-southrows and 2 east-west rows, giving 2 unique permutationsof 2 dimers and 2 solitaires) and for Cube10 10H (5north-south rows, 4 east-west rows, 10 unique permuta-tions of 8 dimers and 4 solitaires). Similar analysis of

Cube1414H (7 north-south rows, 6 east-west rows, 72unique permutations of 18 dimers and 6 solitaires) wasimpractical with available computational resources. Tak-ing 0 = dimer in leftmost position and 1 = dimer shiftedright by one row, then for Cube66H the 2 unique com-binations may be denoted as: 00 (=11) and 01 (=10). ForCube1010H the 10 unique combinations may be denotedas: 0000, 1000 (=0001), 0100 (=0010), 1100 (=0011),1010 (=0101), 1001, 0110, 1110 (=0111), 1101 (=1011),and 1111.

To determine the sensitivity of hydrogenatednanodiamond lattice structure to selective single-atom

depassivation, from 1 to up to 5 neighboring H atoms wereremoved in specific patterns from several representativesurface locations on C(100)H(21) and C(110)H(11)faces of Cube8 8H and on a C(111)H(1 1) faceof Octa12 12H. In another series of runs, surface Hatoms were successively removed from a center locationon each of the three principal crystal planes, in closestproximity to previously created radical sites to observe thethreshold local depassivation required to trigger significantchange in the local diamond lattice structure. Anotherseries looked at neighboring depassivations from vertexlocations. For partial depassivations the smallest possible

multiplicity was used in most cases, i.e., singlet for evenH deletions and doublet for odd H deletions.All studies were conducted using DFT consuming

1,466,852.53 CPU-hours of runtime on the IBM BlueGene/P supercomputer (23 TFlops) installed at MoscowState University, plus 24,000 CPU hours on the JS20cluster (PowerPC 970FX CPUs). Most calculations wereperformed using the Car-Parrinello Molecular Dynamics(CPMD) code,81 a parallelized plane-wave/pseudopotentialimplementation of DFT particularly designed for ab-initio molecular dynamics. Computations were done usingBLYP (Becke, Lee, Yang, Parr) and PBE (Perdew, Burke,

Ernzerhof)82 functionals within the generalized-gradientapproximation (GGA) and ultrasoft, gradient-corrected,Vanderbilt-type pseudopotentials with a kinetic energyplane-wave cutoff of 340 eV using a cubic periodic super-cell in which at least 4 of clearance was left between anyatom and the periodic cell boundary, giving >8 separa-tion between periodic images. (The more common B3LYP

is a hybrid functional containing a Hartree-Fock exchangecomponent, impractical for molecules with extremely largeatom counts.) A few calculations were also performedusing the PRIRODA quantum chemistry code49 that can dofast DFT calculations using the resolution-of-the-identity(RI) approximation to the Hartree-Fock method, support-ing RI-MP2 (second-order Mller-Plesset)83 and coupled-cluster CCSD and CCSD(T) with analytical gradients. InPRIRODA, DFT PBE and MP2 methods were used withthe L1 basis set84 which is an analog of the cc-VDZbasis set. Since the PBE functional gave closer matchto experiment than BLYP in preliminary tests on ten of

the smallest structures, PBE was used almost exclusivelyfor the remaining larger structures. Note that C### inSection 3.4 refers to a specific carbon atom in a refer-enced nanodiamond model available in the supplementalstructure files.

3. RESULTS AND DISCUSSION

3.1. Clean and HydrogenatedNanodiamond Octahedrons

Geometry optimizations of the octahedral nanodiamondsyielded the following results:

Octa2 2H (adamantane). Does not reconstruct (allmethods) (Fig. 3(A)). In this and other cases below, BLYPoverestimates the CC bond length by 0.02 (1.56 )whereas PBE (CPMD, PRIRODA) gives values close toexperiment (1.54 ).

Octa2 2. For the dehydrogenated adamantane cage,geometry optimization using PBE produces a rearrangedclosed-cage structure possessing three 3-member rings (allbut one bondlengths 1.431.46 ), three 5-member rings(all but one bondlengths 1.431.46 ), and one 6-memberring (Fig. 3(B)) with the topmost carbon pair at 1.698 ,indicating 10% bond strain; the structure is mostly sp2,

apparently fullerenized. BLYP produces the same structurebut with the topmost carbon pair debonded (Fig. 3(C)).

Octa44H (Fig. 3(D)), Octa6 6H (Fig. 3(H)). Doesnot reconstruct (all methods).

Octa4 4. CPMD-PBE optimization converges to thevery slightly rounded shape as reported by Barnard et al.37

for C35 crystal with the perimeter bondlengths contract-ing to 1.441.46 (vs. 1.41 from Barnard et al.37;indicating trend toward sp2 and bondlengths to the cen-tral atom extend to 1.631.65 (vs. 1.60 fromBarnard et al.37; indicating increasing sp3 bond strain)(Fig. 3(E)). However, we found that this state (Octa4



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4-config1) is only metastable. (The PRIRODA-PBE opti-mization also passes through this state, but then the cen-tral atom loses its privileged position and bonds to anouter wall atomand the choice of outer wall atom deter-mines the final result.) A short molecular dynamics sim-ulation of Octa4 4-config1 in CPMD (48 fs, 300 K)produced another metastable rearrangement (Octa4 4-

config2) whose energy is lower (CPMD-PBE: 696 eV,

(A)

(E)

(H) (I)

(F) (G)

(B) (C) (D)

Fig. 3. Octahedron, side views: (A) Octa22H (adamantane) (PBE), (B) Octa22 (PBE), (C) Octa22 (BLYP), (D) Octa44H (PBE), (E) Octa44-config1 (PBE), (F) Octa44-config2 (PBE), (G) Octa44-config3 (PBE), (H) Octa66H (PBE), and (I) Octa66 (PBE). (C= black, H=white,Core C Atoms= green).

PRIRODA-HF: 627 eV, PRIRODA-MP2: 122 eV)than Octa4 4-config1 after subsequent optimization(Fig. 3(F)). Continuing this MD annealing process finallyyielded an apparently stable rearrangement (Octa44-config3) whose energy is even lower (CPMD-PBE:1871 eV, PRIRODA-HF: 2557 eV, PRIRODA-MP2:2748 eV) than Octa44-config1 after subsequent opti-

mization (Fig. 3(G)). The structure shown is a hollow



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fullerenic shell (no endohedral atoms) consisting predom-inantly of 6-carbon rings, but including one 5-carbon ring,one 7-carbon ring, and one 11-carbon ring (incorporat-ing two 1.251.26 CC bonds at the top) defining theopen-mouth top of the basket. Relative energy differencesare large because so many bonds are involved in rear-rangements, and because the initial structure is far from

the global minimum and many local minima are avail-able nearby. A normal modes analysis to verify a globalminimum was not attempted because the PES is very com-plex, the three minima identified so far are probably notdirectly connected, and CPMD does not offer the IRCmethod and has no tools to simplify transition state loca-tion analogous to Gaussian QSTN. Optimizing Octa44 using CPMD-BLYP yields a spheroidal shell structure

(A) (B) (C) (D)

(E)

(I) (J) (K)

(F) (G) (H)

Fig. 4. Octahedron, side views: (A) Octa88H (PBE), (B) Octa88 (PBE), (C) Octa1010H (PBE), (D) Octa1010 (PBE), (E) core of Octa1010,(F) Octa1212H (PBE), (G) Octa1212 (PBE), (H) core of Octa1212, (I) Octa1414H (PBE), (J) Octa1414 (PBE), and (K) core of Octa1414.(C= black, H=white, Core C Atoms= green).

composed of nine 6-member rings, one 5- and one 3-member ring, plus two 10-member rings between whichthe central atom has bonded, with at least one CC bond(1.26 ) and two C C bonds (1.36 ) present; the over-all structure is sp2 with most bondlengths in the 1.411.49 range.

Octa66. Using VASP on C84 crystal, Barnard et al.37

report that the 74 surface atoms separate from the 10 innercore atoms with the outer carbon shell containing entirelysp2 bonded atoms (CC bondlengths 1.45 ), the innercore contracting to 1.41 CC bondlengths, with ashellcore separation distance of2.25 37 or 3 .19

Using CPMD-PBE, CPMD-BLYP, and PRIRODA-PBE,we confirm that Octa66 acquires a round shape and sep-arates from an inner core (Fig. 3(I); core atoms shown in



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green) that includes highly strained and pyramidalized Catoms (not a tetrahedral sp3 structure), with a shellcoreseparation distance of2.7 .

Octa8 8H (Fig. 4(A)), Octa10 10H (Fig. 4(C)),Octa12 12H (Fig. 4(F)), Octa14 14H (Fig. 4(I)).CPMD-PBE predicts no reconstruction; all retain the orig-inal cleaved diamond structure with no graphitization ofC(111) surfaces and no significant change in the length ofsurface or interior bonds.

Octa8 8. CPMD-PBE shows this structure optimizesto OLC with 130 fullerenic (sp2 outer shell atoms and 35inner-shell core atoms with a partially sp3 bonding pattern,all with bondlengths in the 1.411.50 range and a shellcore separation distance of2.7 (Fig. 4(B); core atomsshown in green). Barnard et al.37 found a similar octahe-dral carbon-onion structure with a shellcore separationdistance of2.25 , using DFT(VASP) on C165 crystal.CPMD-PBE optimization yielded a few 3-member ringsin both Octa88 and Octa66 structures; DFT(VASP)41

also found 3-member rings on the reconstructed C(111)

(A) (B) (C) (D)

(E) (F) (G) (H)

(I) (J) (K) (L)

Fig. 5. Cuboid, top views: (A) Cube33H (PBE), (B) Cube3 3 (PBE), (C) Cube44H (PBE), (D) Cube44 (PBE), (E) Cube55H (PBE),(F) Cube55 (PBE), (G) Cube55 (MP2), (H) Cube66H (PBE), (I) Cube6 6 (PBE), (J) Cube77H (PBE), (K) Cube77 (PBE), and (L)Cube77 electron density image (side view). (A-K: C = black, H=white, Core C Atoms = green).

surfaces of the similar-sized dehydrogenated octahedraldiamond nanowires C108, C186 and C294.

Octa1010. Reconstructs to bucky-diamond (Fig. 4(D))with a 202-atom sp2 fullerenic outer shell, surroundingan 84-atom sp3 diamondlike inner core (Fig. 4(E)) havinghighly compressed bonds.

Octa1212. Reconstructs to bucky-diamond (Fig. 4(G))with a 290-atom sp2 fullerenic outer shell, surrounding a165-atom sp3 diamondlike inner core (Fig. 4(H)) havinghighly compressed bonds.

Octa1414. Reconstructs to bucky-diamond (Fig. 4(J))with a 397-atom sp2 fullerenic outer shell, surrounding a283-atom sp3 diamondlike inner core (Fig. 4(K)) havinghighly compressed bonds. Using a less-computationallyintensive density functional based tight binding methodwith self-consistent charges (SCC-DFTB), Barnard andSternberg32 also found that the core sp3 region continuesto grow in size relative to the sp2 outer shell for the C969(Octa16 16), C1330 (Octa18 18), and C1771 (Octa20

20) nanodiamond octahedrons.



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3.2. Clean and Hydrogenated Nanodiamond Cuboids

Geometry optimizations of the cuboid nanodiamondsyielded the following results:

Cube3 3H. Does not reconstruct (all methods)(Fig. 5(A)). The dimerization on the C(100) faces in thisand all subsequent hydrogenated cuboids is the only diver-

gence from the regular tessellation pattern of sp3 carbonatoms in the lattice.

(A) (B) (C) (D)

(E) (F) (G) (H)

(I) (J) (K) (L)

(M) (N) (O) (P)

Fig. 6. Cuboid (all PBE), side views: (A) Cube8 8H, (B) Cube8 8, (C) Cube9 9H, (D) Cube9 9, (E) Cube10 10H, (F) Cube10 10,(G) Cube1111H, (H) Cube1111, (I) Cube1212H, (J) Cube1212, (K) Cube1313H, (L) Cube1313, (M) Cube1414H, (N) Cube1414,(O) Cube1515H, and (P) Cube1515. (C= black, H=white).

Cube33. CPMD-PBE optimized structure reconstructsinto an sp2-hybridized structure (possibly metastable) thatincludes two 4-carbon rings, two 5-carbon rings, and six6-carbon rings with no endohedral atoms (Fig. 5(B)).Barnard19 reported that a slightly larger C28 cuboiddecayed to a tetrahedral amorphous structure that must

be metastable, since the fullerene C28 is known to be theglobal energy minimum.



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Cube4 4H (Fig. 5(C)), Cube5 5H (Fig. 5(E)),Cube66H (Fig. 5(H)), Cube77H (Fig. 5(J)). Does notreconstruct (all methods).

Cube44. CPMD-PBE optimized structure reconstructsinto an sp2-hybridized structure (likely only metastable)that includes a 10- and a 12-carbon-chain loop reminiscentof cumulene rearrangement intermediates often seen in theself-assembly of small fullerenes (Fig. 5(D)).

Cube55. CPMD-PBE optimized structure reconstructsinto a fullerenic spheroidal shell, which is separated froman inner core of 5 atoms (Fig. 5(F); core atoms shownin green) two of which are bonded at an ethynyl-likebondlength (1.215 ) and bonded at either end to neigh-boring carbon atoms through ethenyl-like bondlengths(1.36 ). It is likely that this is only a metastable localenergy minimum but we have not investigated the structurefurther. The PRIRODA-MP2 geometry (Fig. 5(G)) is ahighly distorted sp3 lattice that appears transitional becausemany CC bondlengths are fullerenic and the geometryincludes at least four 1.211.24 CC structures.

Cube6 6. CPMD-PBE optimized structure retainssome sp3 bonding connectivity but the outer shell appearsmostly fullerenic (Fig. 5(I)), and two internal voidshave opened inside two neighboring corners due to thenear-pyramidalization of two carbon atoms in an endohe-dral 3-member ring (producing some 9- and 10-memberrings). There is 3- and 4-member ring formation both inter-nally and in the outer shell. This may be a transitionalstructure on the path to graphitization.

Cube7 7. CPMD-PBE optimized structure retains

mostly sp3

bonding connectivity (Fig. 5(K)), though manybonds between core and shell region are highly strainedbonds (and a few of them are broken) and one internalvoid has opened up near one corner (visible at upper leftin the electron density isosurface image of Cube7 7)(Fig. 5(L)).

Cube8 8H (Fig. 6(A)), Cube9 9H (Fig. 6(C)),Cube10 10H (Fig. 6(E)), Cube11 11H (Fig. 6(G)),Cube12 12H (Fig. 6(I)), Cube13 13H (Fig. 6 (K)),Cube14 14H (Fig. 6 (M)), Cube15 15H (Fig. 6(O)).CPMD-PBE predicts no reconstruction; all retain the orig-inal cleaved diamond structure with no graphitization of

C(111) surfaces and no significant change in the length ofsurface or interior bonds.Cube88 (Fig. 6(B)), Cube99 (Fig. 6(D)), Cube10

10 (Fig. 6(F)), Cube11 11 (Fig. 6(H)), Cube12 12 (Fig. 6(J)), Cube13 13 (Fig. 6(L)), Cube14 14(Fig. 6(N)), Cube15 15 (Fig. 6(P)). CPMD-PBE opti-mized structures retain mostly sp3 bonding connectivity,with most interior lattice bondlengths normal for diamond,bonds between core and outermost shell slightly to mod-erately stretched (1.561.68 ), and bonds within the out-most shell somewhat compressed (1.421.52 ). Usinga less-computationally intensive density functional based

tight binding method with self-consistent charges (SCC-DFTB), Barnard and Sternberg32 also found that the alter-native nanodiamond cuboids C259, C712, C881 and C1798 areessentially all sp3-bonded except for a narrow line of atomsalong the C(110)/C(110) edges which have sp2 hybridiza-tion.

These results generally support Barnards contention19

that although there is preferential exfoliation of C(111)surfaces over lower index surfaces on isolated clusters,even fully dehydrogenated nanodiamonds up to 2 nm maybe stable in the absence of C(111) surfaces. Our results,obtained for 0 K, are also consistent with findings byothers8586 using DFTB at finite temperature on similarstructures.

3.3. Dimerization Patterns onNanodiamond C(100) Faces

For C(100) surfaces on cuboids with an odd number of

north-south dimerizable rows (Cube66H, Cube1010H,

00

01

0000

1001

1101

1111

Fig. 7. Representative dimerization patterns on cuboid C(100) facesfor Cube6H(00, 01) and Cube10 10H(0000, 1001, 1101,1111). (C= black, H=white, shifted dimer= green).



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Table II. Geometry-optimized relative energies for dimerization pat-terns on C(100) faces of the 1.5-nm cuboid nanodiamond C428H200(Cube1010H).

Dimerization Relative Dimerization Relativepattern energy (eV) pattern energy (eV)

0000 +0.13 1001 +3.831000 (=0001) +3.80 0110 +4.70

0100 (=0010) +4.40 1110 (=0111) +4.871100 (=0011) +4.47 1101 (=1011) +3.481010 (=0101) +5.30 1111 0.00

and Cube1414H), one north-south row will be unpaired,creating a variety of possible dimerization patterns (Fig. 7).Cube66H-00 is 033 eV lower in energy than Cube66H-01 and Cube6 6-00 is 332 eV lower in energythan Cube66-01. For dimerization patterns on a C(100)face on Cube10 10H, the 0000 pattern with the soli-taire row between two dimer rows is +013 eV higherin energy than the 1111 pattern with the solitaire rownearest the face edge, which appears to be the globalminimum. The mixed-row patterns 1001 and 1101 are+383 eV and +348 eV higher in energy, respectively,than 1111. The relative energies for all ten dimerizationpatterns (Table II) suggest that parallel rows of dimers andsolitaires are significantly preferred to mixed rows con-taining both dimers and solitaires (mixed dimer positionsincrease structural tension). Additionally, solitaire rowsplaced nearest the edge of a face are slightly preferred tosolitaire rows in internal positions.

3.4. Partial Dehydrogenation ofNanodiamond Surfaces

In order to extend a structure using DMS, one or moreneighboring radical sites must be created on a growingpassivated nanodiamond workpiece that is elsewhere com-pletely passivated. These sites exist either after remov-ing one or more H atoms using a positionally-controlledhydrogen abstraction tool or after failing to passivate anexisting radical site using a positionally-controlled hydro-gen donation tool. To address the question of how manyadjacent radical sites may be simultaneously present ona nanodiamond facet before the underlying sp3 lattice

begins to reconstruct, multiple neighboring H atoms wereremoved in specific patterns from representative mid-facet,edge, and vertex locations on a C(111)H(11) face (themost graphitization-prone diamond surface) of the octahe-dron nanodiamond Octa1212H.

In a first series of calculations, hydrogen atoms wereremoved in progressively larger numbers from C(111)octahedral mid-facet positions. The removal of the first Hatom from lattice surface atom C203 (Fig. 8(A)) causes thiscarbon atom to drop slightly lower into the lattice, its threesupporting CC bondlengths decreasing from 1.540 to1.50 . The removal of a second H atom from lattice

surface atom C327 at the 4 oclock position relative toC203 (Fig. 8(B)) causes both C atoms to drop slightlymore, with the CC bond to their one mutual subsur-face neighbor C atom decreasing to 1.473 and theirCC bonds to their two non-mutual subsurface neighborC atoms falling to 1.501 and 1.491 , respectively;removing the second H atom from lattice surface atomC205 at the 2 oclock position (Fig. 8(C)) yields similarbondlengths. Removing the second H atom from latticesurface atom C306 at the 8 oclock position (Fig. 8(D))causes the six CC lattice bonds to the two depassivated Catoms to compress slightly to 1.494 but all neighboringbonds remain unchanged near 1.540 . Removal of 3Hatoms in a triangle pattern from C203, C205, and C317 (whichlies at 3 oclock relative to C203) (Fig. 8(E)) yields CCbondlengths to the mutual subsurface C atom of 1.501 ;for interior atom C205 the other two CC bondlengths are1.501 and 1.502 , whereas for the endmost atoms C203and C317 the other two CC bondlengths are 1.503 and

1.506 . There are only negligible changes in the in-planeCC bondlengths immediately peripheral to the C203C205C317 triad, but one isolated cross-plane CC bond betweenatoms C204 and C206 (below C205) moderately stretches to1.658 .

Removing 4H atoms in a parallelogram pattern fromcarbon atoms C203, C205, C317 and C235 (Fig. 8(F)) causesmore significant lattice distortion. (The same atoms appearas a square pattern when camera position is moved toa different vertex; Fig. 8(G)) The CC bondlength to themutual subsurface C atom (C204) shared by 3 dehydro-genated C atoms averages 1.475 with in-plane bond

angles increasing from the relaxed tetrahedral 109.5 toa slightly strained 118. The CC bondlengths to themutual subsurface C atom (C318) shared by 2 dehydro-genated C atoms average 1.477 . The seven remain-ing CC bondlengths between the four dehydrogenated Catoms and their neighboring subsurface C atoms average1497 0005 . The in-plane CC bondlengths immedi-ately peripheral to the parallelogram are largely unchanged;immediately underneath the dehydrogenated pattern thecross-plane CC bondlengths are modestly stretched, in the1.551.59 range, but this cross-plane strain is largelyabsent from the next-deepest layer under the pattern. How-

ever, the cross-plane bond between C318 and C322 (belowC235) is stretched to 1.701 and the cross-plane bondbetween C204 and C206 (below C205) is highly stretched to1.823 (close to the 1.87 Morse bond scission distancefor CC), indicating incipient rearrangement near the twomutually shared C204 and C318 atoms.

Removing 4H atoms in a 3-in-line pattern from atomsC214, C203, C317and C205 (Fig. 8(H)) produces similarsignificant lattice distortion. The CC bondlength to themutual subsurface C atom (C204) shared by 3 dehydro-genated C atoms averages 1.469 with in-plane bondangles again increasing to a slightly strained 119. The



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CC bondlengths to the mutual subsurface C atom (C227)shared by 2 dehydrogenated C atoms average 1.470 .The seven remaining CC bondlengths between the fourdehydrogenated C atoms and their neighboring subsur-face C atoms average 1.500 0.004 . The in-plane CCbondlengths immediately peripheral to the parallelogramare largely unchanged; immediately underneath the dehy-

drogenated pattern the cross-plane CC bondlengths aremodestly stretched, in the 1.551.59 range. However,the cross-plane bond between C227 and C228 (below C214)is stretched to 1.735 and the cross-plane bond betweenC204 and C206 (below C203) is stretched to 1.849 (close tothe 1.87 Morse bond scission distance for CC), againindicating incipient rearrangement.

Increasing the number of neighboring dehydrogenationsto 5H atoms (Fig. 8(I)) produces an optimized struc-ture very similar to the 4-atom removal pattern shownin Figure 8(F) but apparently lacking high-strain CCbondlengths exceeding 1.634 . A short (24 fs) MD simu-

lation at 300 K yields no rearrangements of this structure.

(A) (B) (C) (D)

(E)

(I)

(F) (G) (H)

Fig. 8. Removal of H atoms from mid-facet positions on C(111)H-(1 1) face of Octa1212H (top view, 2.3 nm edge length, init. 651 atoms):removed 1 atom (A); 2 atoms in line toward edge (B), parallel to edge (C), or separated by one row (D); 3 atoms nearest-neighbor (E); 4 atomsnearest-neighbor parallelogram (F), nearest-neighbor square (G), or 3-in-line (H); and 5 atoms nearest-neighbor (I). (C = black, H=white).

The surface transformation to onion-like geometry mayinvolve changing the conformation from concave toconvex for surface fragment carbon atoms possess-ing interlayer bonds, in which case the complete recon-struction of a surface fragment probably requires passingthrough a number of intermediate states. For instance, ina calculation started from one such possible intermediate

state in which the C204C206 distance is initialized at 3 ( double the normal CC bondlength), atom C206 remainsin the convex geometry after structure optimization, dur-ing which the C204C206 distance stabilizes at 2.403 (well above the normal 1.54 CC bondlength, indicat-ing a broken bond), yielding an intermediate graphitizedstate that lies 0.43 eV higher in energy than the optimizedstructure shown in Figure 8(I). However, a complete anal-ysis of intermediate states that lead to graphitization isbeyond the scope of this work.

In a second series of calculations, hydrogen atoms wereremoved in progressively larger numbers along C(111)

octahedral edge positions. The removal of the first H atom



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from lattice surface atom C216 (Fig. 9(A)) causes the car-bon atom to drop slightly lower into the lattice, its threeCC bondlengths decreasing from 1.540 to 1.500 .

The removal of a second H atom from lattice surfaceatom C211 along the edgeline (Fig. 9(B)) causes both C216and C211 to drop slightly more, with the CC bondlengthsto their one mutual subsurface neighbor C atom decreasing

to 1.465 , the CC bondlengths to their two non-mutualsubsurface neighbor C atoms falling to 1.493 , and thecross-plane bonds below atoms C216 and C211 stretchingslightly to 1.57 . Removing the second H atom from lat-tice surface atom C205 above the edge (Fig. 9(C)) yieldssimilar bondlength changes (mutual bondlengths to atomC218 at 1.472 , nonmutual bondlengths 1.491 ), butone isolated cross-plane CC bond between atoms C218and C219 (below C216) stretches to 1.724 . Removingthe second H atom from lattice surface atom C217 belowthe edge (Fig. 9(D)) allows a 1.384 C C bond toform between C216 and C217 as typically happens when

two mutually-bonded C atoms are both dehydrogenated.

(A) (B) (C) (D)

(E) (F)

(I)

(G) (H)

Fig. 9. Removal of H atoms from edge positions along C(111)H-(1 1) face of Octa1212H (top view, 2.3 nm edge length, init. 651 atoms):removed 1 edge atom (A); 2 atoms in line along edge (B) 1 above edge (C), or 1 below edge (D); 3 atoms, in line along edge (E) 2 above edge (F), or1 below edge (G); 4 atoms, 2 in line along edge and 2 below edge (H); and 5 atoms, 3 in line along edge and 2 below edge (I). (C = black, H=white).

The C C dimer drops just slightly into the lattice as thefour CC bonds supporting either end of the dimer declinein length to 1.51 , while the cross-plane CC bondsbetween atoms C218 and C219 (below C216) and betweenatoms C220 and C221 (below C217) stretch moderately to1.622 .

The removal of a third H atom from lattice surface atom

C18 along the edgeline defined by C216 and C211 (Fig. 9(E))causes all three dehydrogenated C atoms to drop slightlyinto the lattice, with the CC bondlengths to their three lat-tice support atoms decreasing to an average 1.500 (C211),1.498 (C216) and 1.500 (C18), and the three cross-planeCC bonds underneath each of the three dehydrogenatedatoms stretching slightly to an average 1.576 . Remov-ing H atoms from C205, C216and C226 with two C atomsabove the edge (Fig. 9(F)) gives a triangle pattern simi-lar to Figure 8(D), with CC bondlengths to the mutualsubsurface C atom (C218) of 1.502 , bondlengths to thenonmutual support atoms of 1.500 , negligible changes

in the in-plane CC bondlengths immediately peripheral



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(A) (B) (C)

Fig. 10. Removal of H atoms from vertex junction of four C(111)H-(11) faces of Octa1212H (top view, 2.3 nm edge length, init. 651atoms): removed 2 atoms from apical C atom (A); 4 atoms, 2 from apicalC atom and 2 from two side C atoms (B); and 8 atoms, 2 from apicalC atom and 6 from nearest-neighbor side C atoms (C). (C = black, H=white).

to the C205C216C326triad, and one isolated cross-planeCC bond

between atoms C218 and C219 (below C216) moderatelystretched to 1.659 . Removing H atoms from C216, C217and C211 with one C atom below the edge (Fig. 9(G))yields a line of three dehydrogenated mutually-bonded Catoms with 1.424 bondlengths; the local structure appar-ently adopts sp2 hybridization because the three C atomsare unable to form two adjacent C C bonds. Atoms C216and C211 have 1.504 bonds to two C atoms at eitherend; center atom C217 has a 1.577 bond to the C atombeneath it, which in turn has two 1.522 CC bonds andone modestly stretched 1.597 bond to its three neigh-boring C atoms, but there are no other lattice distortionsof significance.

(A)

(E) (F) (G)

(B) (C) (D)

Fig. 11. Removal of H atoms from locations along a C(100)H-(11)/C(110)-H(11) edge of Cube88H (top view of C(100), 1.2 nm edge length,init. 380 atoms): removed 1 atom, south edge (A); 2 atoms, south edge and west edge (B), south edge and north-south row (C), or same north-southrow (D); 3 atoms, south edge, west edge and north-south row (E). Also, removal of H atoms from locations on a C(110)H(1 1) face of Cube88H:3 atoms removed along a trough (F), 3 atoms removed along a ridge (G). (C = black, H=white).

Removing four H atoms from C19, C216, C217and C211with two C atoms below the edge (Fig. 9(H)) yields a chainof four dehydrogenated C atoms, with two pairs double-bonded as -C CC C- having interior bondlengths1.394 , 1.451 , and 1.395 , respectively. (The sin-glet lies 080 eV below the triplet multiplicity for thisstructure.) There are also two CC bonds directly beneathC19 and C217 in the C(111) cross-plane direction that arestretched to an average 1.622 , indicating a growingpotential for graphitization, but the cross-plane stretchedregion is still too small to seriously deform the lattice.

Removing five H atoms from C18, C19, C216, C217andC211 with two C atoms below the edge (Fig. 9(I)) yieldsa chain of five dehydrogenated C atoms with averageCC bondlengths 1.425 (vs. 1.545 for neighboringCC bonds), cross-plane bondlengths averaging 1.507 (vs. 1.546 ) to the second layer and two cross-planebondlengths stretched to 1.629 to the third layer, butstill no evidence for outright graphitization.

In a third series of calculations, hydrogen atoms wereremoved in progressively larger numbers from C(111)octahedral vertex positions. Removing both H atomsfrom the apical carbon atom C429 (Fig. 10(A)) reducesbondlength to its two lattice C atoms (C455, C428) to anaverage 1.487 , and the bonds to the four C atoms (C 313,C454, C422, C430) below C455 and C428 stretch very slightlyto 1.566 . Removing four H atoms, two from the api-cal C429 and one each from carbon atoms C455 and C313immediately below C429 (Fig. 10(B)) produces compressed



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1.406 bonds between C429C455and C455C313, and amoderately stretched 1.604 bond between C428C430.Removing four more H atoms from the next lowest fourC atoms, for a total of 8H atom removals (Fig. 10(C)),produces an asymmetric tip with 1.411 (C429C428) and1.488 (C429C455) CC bonds to apical atom C429. Thetwo CC bonds beneath C428 average 1.458 below whichthe next four CC lattice bonds average 1.512 , and thetwo CC bonds beneath C455 average 1.413 below whichthe next four CC lattice bonds average 1.528 . Betweenthe 4th and 5th planes, atom C316 which lies directly belowC429 in the lattice framework has two CC bonds stretchedto 1.624 , but all other bonds in the lattice appear near the1.540 average and the entire lattice geometry remainsintact.

In a fourth set of calculations, one (Fig. 11(A)), two(Fig. 11(B), Fig. 11(C), Fig. 11(D)) and three (Fig. 11(E))H atoms were removed from locations along a C(100)H-(1 1)/C(110)H(1 1) edge of the cuboid nanodia-mond Cube88H. Bondlengths between dehydrogenatedC atoms decreased to the 1.391.45 range but the latticegeometry was not disrupted.

There is no evidence or suggestion in the experi-mental or theoretical literature that the structure of theC(110)H(11) surfaces of a cuboid nanodiamond mightbe changed by altering the surface passivation pattern.Nevertheless, one last set of calculations was performedin which three H atoms were removed from a C(110)H(11) surface along a trough (Fig. 11(F)) where there isno possibility of change in bond order (CC bondlengthsto dehydrogenated atoms along ridge contract only slightly

to 1.471.50 ; one CC bond from the CH betweenthe two dehydrogenated ridge carbons, down into the lat-tice, stretches to 1.639 ), and along a ridge (Fig. 11(G))where a change in bond order (to pi chain) is expectedand is observed (CC bondlengths along ridge: 1.550 1.509 1.426 1.427 1.509 1.551 ; dehydro-genated atom bondlengths down into the lattice declineslightly from 1.553 to 1.512 ). No pathological recon-structions were observed in either case.

4. CONCLUSIONS

Computational studies using Density Functional Theory(DFT) have determined that fully hydrogenated nanodia-monds up to 2 nm (9001800 atoms) in size having onlyC(111) faces (octahedrons) or only C(110) and C(100)faces (cuboids) maintain stable sp3 hybridization. Fullydehydrogenated cuboid nanodiamonds above 1 nm retainthe diamond lattice pattern, but smaller dehydrogenatedcuboids and dehydrogenated octahedron nanodiamonds upto 2 nm reconstruct to bucky-diamond or onion-like car-bon (OLC). Up to three adjacent passivating H atomsmay be removed from mid-facet locations on the most

graphitization-prone C(111) face of an octahedron nan-odiamond without reconstruction of the underlying dia-mond lattice; removal of a fourth or fifth H atom increases12 cross-plane bondlengths indicating incipient graphiti-zation. H atom removals from an even number of adja-cent mutually-bonded C atoms along octahedral edges willform C C bonds; aside from this change in bond order,

up to five H removals along edges will moderately stretch12 cross-plane bondlengths but will not disrupt the octa-hedron diamond lattice. Removing up to 8H atoms fromvertex locations on a nanodiamond octahedron, and Hremovals from C(100) or C(110) surfaces in compact pat-terns, also produce no lattice reconstructions. On C(100)surfaces of cuboid nanodiamonds, parallel rows of carbondimers and solitaires are energetically preferred to mixedrows containing both dimers and solitaires, and solitairerows placed nearest the edge of a face are slightly pre-ferred to solitaire rows located at interior positions on theface.

We conclude that fully- and mostly-H-passivated simplecuboid and octahedral diamond nanoparts possess at leaststatic structural stability. These results support the con-servative DMS fabrication strategy outlined in Freitas andMerkle1 wherein atomically precise diamond nanopartsare fabricated using reaction sequences that minimize thenumber of exposed surface radicals during any intermedi-ate phase of a mechanosynthetic operation, and whereinall surfaces are kept fully hydrogenated at all times duringfabrication except for single-site dehydrogenations that arerequired to complete an addition or attachment (e.g., ringclosing) operation.

Acknowledgments: The authors acknowledge com-ments on an earlier version of the manuscript by AmandaS. Barnard and graphics assistance by Damian G. Allis.Robert A. Freitas, acknowledges private grant supportfor this work from the Life Extension Foundation, theKurzweil Foundation, and the Institute for MolecularManufacturing.

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Received: 30 March 2010. Accepted: 2 May 2010.

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